New advances in genomic technology make it possible to address some of the most fundamental questions in biology for the first time. They also highlight a need for new approaches to analyze and model massive amounts of complex data. In this thesis, I present six research projects that illustrate the exciting interaction between high-throughput genomic experiments, new machine learning algorithms, and mathematical modeling. This interdisci- plinary approach gives insights into questions ranging from how variations in the epigenome lead to diseases across human populations to how the slime mold finds the shortest path. The algorithms and models developed here are also of interest to the broader machine learning community, and have applications in other domains such as text modeling.